Spectra of perfect state transfer Hamiltonians on fractal-like graphs
Abstract
In this paper we study the spectral features, on fractal-like graphs, of Hamiltonians which exhibit the special property of perfect quantum state transfer (PQST): the transmission of quantum states without dissipation. The essential goal is to develop the theoretical framework for understanding the interplay between PQST, spectral properties, and the geometry of the underlying graph, in order to design novel protocols for applications in quantum information science. We present a new lifting and gluing construction, and use this to prove results concerning an inductive spectral structure, applicable to a wide variety of fractal-like graphs. We illustrate this construction with explicit examples for several classes of diamond graphs.
- Publication:
-
Journal of Physics A Mathematical General
- Pub Date:
- March 2021
- DOI:
- 10.1088/1751-8121/abc4b9
- arXiv:
- arXiv:2003.11190
- Bibcode:
- 2021JPhA...54l5301M
- Keywords:
-
- quantum information;
- functional analysis;
- spectral theory;
- fractals;
- Mathematical Physics;
- Computer Science - Information Theory;
- Mathematics - Functional Analysis;
- Mathematics - Spectral Theory;
- Quantum Physics;
- 81Q35 81P45 94A40 05C50 28A80
- E-Print:
- revised version